Ante-Nicene Fathers Volume 5
Hippolytus: The Refutation of All Heresies
Most of the heresies mentioned so far have been heresies from the past. Now Hippolytus is going to dig into modern-day heresies and expose their errors. The method, however, will be the same: survey their beliefs and expose where those beliefs are drawn from pagan sources.
Noetus, Epigonus, and Cleomenes spread in Rome the heresy of the Heraclitian philosophy. They even managed to seize the leadership of the church in Rome and the office of bishop [later to become "Pope"] in the persons of Zephyrinus and Callistus. "Heraclitus then says that the universe is one, divisible and indivisible; generated and ungenerated; mortal and immortal; reason, eternity; Father, Son, and justice, God." In other words, contradictions rule the doctrine under this system, with only Reason stretching over all things. Unfortunately, we do not have access to this universal Reason (so much is Heraclitus, along with other certain doctrines and eschatologies). Christ, in this view, comes to give us access to this universal Reason. This in turn collapses the Son into the Father, since Reason is indivisible.
In practice, these false teachings lead to laxity in church life and practice. Hippolytus stood opposed to those (especially Callistus and Zephyrinus) who taught this, and in turn was accused of rigidity and ditheism. Hippolytus gives a long survey of the life and thought of Callistus (at least compared to the other heresies heretofore mentioned), and declares him a heretic and unfit to lead the church--especially in matters of doctrine and and practice.
The heresy of Elchasai, taken from Pythagoras, claims to be based on a book dictated by a male apparition (Jesus) and a female apparition (the Holy Spirit), which reforms both doctrine and practice, especially baptism. Elchasai teaches in this case baptismal regeneration, especially for the most severe sins. This in turn becomes odd practice--baptism as a means of exorcism or physical healing, if only it's done enough (40+ times).